The heights of women aged 20 – 29 in the United States are approximately Normal with mean 64.2 inches and standard deviation 2.8 inches. The heights of men aged 20 – 29 in the United States are approximately Normal with mean 69.4 inches and standard deviation 3.0 inches. What is the ????‑score for a woman 5.5 feet tall? (Enter your answer rounded to two decimal places.) ????= .64 What is the ????‑score for a man 5.5 feet tall? (Enter your answer rounded to two decimal places.) ????= -1.13 What information do the ????‑scores give that the original non‑standardized heights do not? The ????‑scores show that the woman is slightly different from the average, while the man is very different from the average. The ????‑scores show us that the woman is slightly shorter than average, while the man is much taller than average. The ????‑scores do not give us any additional information, since we already know that the man and woman have equal heights. The ???? ‑scores show us t
Accepted Solution
A:
Answer:a) 0.64b) -1.13 Step-by-step explanation:We are given the following information in the question:Women:Mean, μ = 64.2 inches Standard Deviation, σ = 2.8 inchesWe are given that the distribution of heights of women is a bell shaped distribution that is a normal distribution.Men:Mean, μ = 69.4 inches Standard Deviation, σ = 3.0 inchesWe are given that the distribution of heights of men is a bell shaped distribution that is a normal distribution.Formula:[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]5.5 feet = 66 inchesa) z‑score for a woman 5.5 feet tall[tex]x = 66\\\\\Rightqrrow z = \displaystyle\frac{66 - 64.2}{2.8} = 0.64[/tex]b) z‑score for a man 5.5 feet tall[tex]x = 66\\\\\Rightqrrow z = \displaystyle\frac{66 - 69.4}{3.0} = -1.13[/tex]